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anonymous

2 years ago

Two graphs are shown below:
graph A shows scatter points 1, 3 and 2, 5 and 3, 7 and 4, 9 and 5, 11graph A shows scatter points 1, 11 and 2, 9 and 3, 7 and 4, 5 and 5, 3
Which scatter plot shows a linear relationship between x and y?
Only graph A
Only graph B
Both graph A and graph B
Neither graph A nor graph B

anonymous

2 years ago

Here is the graph:
http://prntscr.com/88hmnm

SolomonZelman

2 years ago

You can see if the points have a pattern
(x,y) \(\Longrightarrow\) (x+a)(y+b)

So we have showed that the pattern here is indeed:
(x,y) \(\Longrightarrow\) (x+\(\color{red}{1}\))(y+\(\color{blue}{2}\))
So each time you are adding 1 to the x, you are adding 2 to the y.
(Saying as the grph goes \(\color{red}{1}\) unit right, it goes \(\color{blue}{2}\) units up)
(lets call change in x, \(\Delta x\) AND lets call change in y, \(\Delta y\) )
\({\rm m}~=~\dfrac{\Delta y}{\Delta x}=\dfrac{\color{blue}{2}}{\color{red}{1}}=\bf 2\)
So the set of point A, is a line with a slope of 2:)